The striker, who has netted 14 goals in the Greek Super League and impressed in the Champions League this season, is set to join the London side for a joint club-record fee
Fulham are on the verge of completing the £11.5 million signing of Olympiakos striker Kostas Mitroglou, Goal understands.
The Cottagers are currently struggling at the wrong end of the Premier League table and are prepared to equal the club-record fee they paid for Steve Marlet back in 2001.
Mitroglou currently leads the scoring charts in Greece with 14 goals and is enjoying an impressive Champions League campaign, scoring a hat-trick against Anderlecht as Olympiakos qualified from the group stages to set up a last-16 tie against Manchester United.
Fulham appear to have won the battle to maintain the services of Tottenham target Dimitar Berbatov but possess one of the weakest attacks in the division and are in need of reinforcements, particularly after allowing Bryan Ruiz to leave for PSV earlier this month.
At the back, Rene Meulensteen has been vocal in his desire to sign both West Ham starlet Ravel Morrison and Swansea left-back Neil Taylor.
The Hammers have valued the former Manchester United midfielder at £10m, with Fulham expected to launch another bid before Friday's deadline.
Meulensteen has confirmed a bid has been submitted for Taylor, but as of Friday there have been no further official updates.